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\author{五六七 }
\title{体能数据偏最小二乘回归 }

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\begin{document}

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\begin{abstract}
对20个健身者的体能数据进行偏最小二乘回归分析。
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\section{问题描述}
某健身俱乐部的20位健身者的体能训练数据如表所示\footnote{数据来源：Linnerud: }。其中第一组是身体特征指标，包括体重、腰围和脉搏。
第二组是训练结果指标，包括单杠、弯曲和跳高。请对这些数据进行偏最小二乘回归分析。

\begin{table}[ht!]\centering
\caption{体能训练数据} \vspace{0.2cm}
\begin{tabular}{|M{1.5cm}|M{1.5cm}|M{1.5cm}|M{1.5cm}|M{1.5cm}|M{1.5cm}|M{1.5cm}|}\hline 
序号 & 体重 $x_1$ & 腰围 $x_2$ & 脉搏 $x_3$ & 单杠 $y_1$ & 弯曲 $y_2$ & 跳高 $y_3$  \\ \hline 
1	&	191	&	36	&	50	&	5	&	162	&	60		\\ \hline 
2	&	189	&	37	&	52	&	2	&	110	&	60		\\ \hline 
3	&	193	&	38	&	58	&	12	&	101	&	101		\\ \hline 
4	&	162	&	35	&	62	&	12	&	105	&	37		\\ \hline 
5	&	189	&	35	&	46	&	13	&	155	&	58		\\ \hline 
6	&	182	&	36	&	56	&	4	&	101	&	42		\\ \hline 
7	&	211	&	38	&	56	&	8	&	101	&	38		\\ \hline 
8	&	167	&	34	&	60	&	6	&	125	&	40		\\ \hline 
9	&	176	&	31	&	74	&	15	&	200	&	40		\\ \hline 
10	&	154	&	33	&	56	&	17	&	251	&	250		\\ \hline 
11	&	169	&	34	&	50	&	17	&	120	&	38		\\ \hline 
12	&	166	&	33	&	52	&	13	&	210	&	115		\\ \hline 
13	&	154	&	34	&	64	&	14	&	215	&	105		\\ \hline 
14	&	247	&	46	&	50	&	1	&	50	&	50		\\ \hline 
15	&	193	&	36	&	46	&	6	&	70	&	31		\\ \hline 
16	&	202	&	37	&	62	&	12	&	210	&	120		\\ \hline 
17	&	176	&	37	&	54	&	4	&	60	&	25		\\ \hline 
18	&	157	&	32	&	52	&	11	&	230	&	80		\\ \hline 
19	&	156	&	33	&	54	&	15	&	225	&	73		\\ \hline 
20	&	138	&	33	&	68	&	2	&	110	&	43		\\ \hline 
\end{tabular}
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\section{建立模型}




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\section{编程计算}




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\section{检验模型}




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\section{回答问题}




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%\section{参考文献 }
\begin{thebibliography}{99}

%\bibitem{dingtongren} 丁同仁、李承治，常微分方程教程，高等教育出版社，2022年3月第三版。
\bibitem{sishoukui-2} 司守奎,孙玺菁. \emph{Python数学建模算法与应用}, 国防工业出版社. 2022年1月第1版. 
\bibitem{hexiaoqun-ara} 何晓群. \emph{应用回归分析(R语言版)}. 电子工业出版社. 2017年7月第1版. 
%\bibitem{dalgaard} Peter Dalgaard 著, 郝智恒等译. \emph{R语言统计入门}. 人民邮电出版社. 2014年6月第1版. 


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